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%I #32 Dec 28 2017 10:34:02
%S 12,15,33,63,72,132,240,273,495,897,1020,1848,3348,3807,6897,12495,
%T 14208,25740,46632,53025,96063,174033,197892,358512,649500,738543,
%U 1337985,2423967,2756280,4993428,9046368,10286577,18635727,33761505,38390028,69549480
%N Numbers k such that k is the altitude of a Heronian triangle with sides m - 11, m, m + 11.
%C a(n) gives the values of y satisfying 3*x^2 - y^2 = 363; corresponding x values are given by A296795.
%C a(n)/3 is the radius of the inscribed circle.
%H Colin Barker, <a href="/A296796/b296796.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4,0,0,-1).
%F From _Colin Barker_, Dec 22 2017: (Start)
%F G.f.: 3*(4 + 5*x + 11*x^2 + 5*x^3 + 4*x^4) / (1 - 4*x^3 + x^6).
%F a(n) = 4*a(n-3) - a(n-6) for n>5.
%F (End)
%e If the sides are 17, 28, 39 the triangle has the altitude 15 against 28 and is a part of the Pythagorean triangle with the sides 15, 36, 39, so 15 is a term.
%t CoefficientList[Series[3 (4 + 5 x + 11 x^2 + 5 x^3 + 4 x^4)/(1 - 4 x^3 + x^6), {x, 0, 35}], x] (* _Michael De Vlieger_, Dec 22 2017 *)
%o (PARI) Vec(3*(4 + 5*x + 11*x^2 + 5*x^3 + 4*x^4) / (1 - 4*x^3 + x^6) + O(x^40)) \\ _Colin Barker_, Dec 22 2017
%K nonn,easy
%O 0,1
%A _Sture Sjöstedt_, Dec 20 2017
%E More terms from _Colin Barker_, Dec 22 2017
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